Question

graph the image of △abc after a translation 1 unit left and 6 units up.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$, a translation 1 unit left and 6 units up changes it to $(x - 1,y+6)$.

Step2: Find new coordinates of point A

Let's assume the coordinates of point A are $(-6,1)$. After translation, the new - x - coordinate is $-6-1=-7$ and the new - y - coordinate is $1 + 6=7$. So the new coordinates of A are $(-7,7)$.

Step3: Find new coordinates of point B

Let's assume the coordinates of point B are $(-5,3)$. After translation, the new - x - coordinate is $-5-1=-6$ and the new - y - coordinate is $3 + 6=9$. So the new coordinates of B are $(-6,9)$.

Step4: Find new coordinates of point C

Let's assume the coordinates of point C are $(-2,-1)$. After translation, the new - x - coordinate is $-2-1=-3$ and the new - y - coordinate is $-1 + 6=5$. So the new coordinates of C are $(-3,5)$.

Step5: Graph the new triangle

Plot the points $A'(-7,7)$, $B'(-6,9)$ and $C'(-3,5)$ on the coordinate - plane and connect them to form $\triangle A'B'C'$.

Answer:

Graph the points $(-7,7)$, $(-6,9)$ and $(-3,5)$ and connect them to form the image of $\triangle ABC$ after the given translation.